Method for determining equivalent thermal conditions between liquid chromatography systems

ABSTRACT

Described is a method of transferring a chromatographic method between liquid chromatography (LC) systems. The method is based on a determination of an isoretention temperature at which two solutes co-elute. The method enables separations to be performed using different LC systems with reproducible and equivalent results. For example, the method allows for a chromatography method developed for HPLC to be more readily transferred to a UPLC system and for a chromatography method developed for a UPLC system to be more readily transferred to a HPLC system. The method addresses LC systems having column ovens of different design in which the internal column temperatures are not equal although the operating temperatures of the column ovens may be accurately controlled to equal values. The retention behavior and resolution of different LC systems is caused to be substantially the same so that equivalent separation results are obtained.

RELATED APPLICATION

This application claims the benefit of the earlier filing date of U.S.Provisional Patent Application Ser. No. 61/297,984, filed Jan. 25, 2010and titled “Equivalent Thermal Conditions in Different HPLC and UHPLCSystems for Transfer of Chromatography Methods,” the entirety of whichis incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates generally to a method for determining equivalentthermal conditions between or among chromatographic systems. Moreparticularly, the invention relates to control of column temperatures toobtain equivalent elution of common samples regardless of the particularchromatographic system used to perform a separation.

BACKGROUND

The control of column temperature is important to the resolvingefficiency of a liquid-chromatography (LC) column regardless of whetherthe system is designed to operate isothermally or by temperatureprogrammed analysis. Column temperature control is commonly achieved byheating of the column, for example, in a convection oven or in an ovenwith still air.

Some chromatographic systems utilize a column heater to control columntemperature. For example, the column may be located in a temperaturecontrolled chamber. The temperature of the fluid mixture or mobile phaseprovided to the column may not be constant, especially for long (e.g.,multi-hour) chromatographic runs where the variations in roomtemperature are significant. Temperature variations can adversely impactthe accuracy of the chromatographic analysis. In some systems, a deviceis used to pre-heat the mobile phase before the mobile phase is injectedinto the column to reduce column inlet fluid temperature fluctuations.

The design of the column oven is typically different for differentchromatographic systems. The particular design used is based, in part,on the requirement to achieve stable retention times and separationmetrics (e.g., selectivity, peak shape and column efficiency) despitevariations in the ambient temperature; however, variances in the designscan lead to differences in chromatographic results when separations ofidentical samples are performed on different LC systems.

SUMMARY

In one aspect, the invention features a method of transferring achromatographic method between LC systems. The method includesdetermining an isoretention temperature of a first LC system at which afirst solute and a second solute in a mobile phase of the first LCsystem co-elute from a column. An isoretention temperature of a secondLC system at which the first solute and the second solute in a mobilephase of the second LC system co-elute from a column is determined. Acolumn offset temperature for transferring a chromatographic methodbetween the first and second LC systems is determined based on thedifference in the isoretention temperatures of the first and second LCsystems.

In another aspect, the invention features a method of transferring achromatographic method between LC systems. According to the method, fora plurality of solute pairs each having a first solute and a secondsolute, a determination of an isoretention temperature of a first LCsystem at which the first solute and the second solute in a mobile phaseof the first LC system co-elute from a column is made. An isoretentiontemperature of a second LC system at which the first solute and thesecond solute in a mobile phase of the second LC system co-elute from acolumn is determined for each of the solute pairs. A column offsettemperature for transferring a chromatographic method between the firstand second LC systems based on the difference in a respective pair ofisoretention temperatures of the first and second LC systems isdetermined for each solute pair.

In another aspect, the invention features a method of transferring achromatographic method between LC systems. According to the method, avan't Hoff functional relationship for a first solute in a mobile phasefor a plurality of column temperatures for a first LC system isdetermined and a van't Hoff functional relationship for a second solutein a mobile phase for a plurality of column temperatures for the firstLC system is determined. An isoretention temperature of the first LCsystem for the first and second solutes is determined as a temperatureat which a retention factor of each of the van't Hoff functionalrelationships of the two solutes in the first LC system are equal. Avan't Hoff functional relationship for the first solute in a mobilephase for a plurality of column temperatures for a second LC system isdetermined and a van't Hoff functional relationship for the secondsolute in a mobile phase for a plurality of column temperatures for thesecond LC system is determined. An isoretention temperature of thesecond LC system for the first and second solutes is determined as atemperature at which a retention factor of each of the van't Hofffunctional relationships of the two solutes in the second LC system areequal. A column offset temperature for transferring a chromatographicmethod between the first and second LC systems is determined based onthe difference in the isoretention temperatures of the first and secondLC systems.

In another aspect, the invention features method of transferring achromatographic method between LC systems. According to the method, foreach solute in a plurality of first solutes, a van't Hoff functionalrelationship for the first solute in a mobile phase for a plurality ofcolumn temperatures for a first LC system is determined and, for eachsolute in a plurality of second solutes, a van't Hoff functionalrelationship for the second solute in a mobile phase for a plurality ofcolumn temperatures for the first LC system is determined. For aplurality of solute pairs each including one of the first solutes andone of the second solutes, an isoretention temperature of the first LCsystem is determined as a temperature at which a retention factor of thevan't Hoff functional relationships of the respective first and secondsolutes in the first LC system are equal.

For each of the first solutes, a van't Hoff functional relationship forthe first solute in a mobile phase for a plurality of columntemperatures for a second LC system is determined and, for each of thesecond solutes, a van't Hoff functional relationship for the secondsolute in a mobile phase for a plurality of column temperatures for thesecond LC system is determined. For each of the solute pairs, anisoretention temperature of the second LC system is determined as atemperature at which the retention factor of the van't Hoff functionalrelationships of the first and second solutes in the second LC systemare equal. For each of the solute pairs, a column offset temperature fortransferring a chromatographic method between the first and second LCsystems is determined based on a difference in a respective pair ofisoretention temperatures of the first and second LC systems.

In still another aspect, the invention features a sample for determiningan isoretention temperature of a LC system. The sample includes asolvent and a solute pair. The solute pair includes two solutesdissolved in the solvent. The solute pair is predetermined to have atemperature at which the two solutes co-elute from a column of a LCsystem.

In yet another aspect, the invention features a sample for determiningisoretention temperatures of a LC system. The sample includes a solventand a plurality of solute pairs. Each of the solute pairs includes twosolutes dissolved in the solvent and has a temperature at which the twosolutes co-elute from a column of a LC system. The temperature forco-elution for each solute pair is different from the temperatures forco-elution for each of the other solute pairs.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and further advantages of this invention may be betterunderstood by referring to the following description in conjunction withthe accompanying drawings, in which like numerals indicate likestructural elements and features in the various figures. For clarity,not every element may be labeled in every figure. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 graphically illustrates the temperature-dependent retention timesfor a separation of two solutes in a LC system.

FIG. 2 is a flowchart representation of an embodiment of a method fordetermining a difference in average column temperatures for twochromatographic systems according to the invention.

FIG. 3 graphically illustrates the separation factor as a function ofcolumn temperature for four solute pairs.

FIG. 4 is a flowchart representation of another embodiment of a methodfor determining a difference in average column temperatures for twochromatographic systems according to the invention.

FIG. 5 graphically illustrates plots based on the van't Hoff equationfor the four solutes of FIG. 3.

DETAILED DESCRIPTION

Reference in the specification to “one embodiment” or “an embodiment”means that a particular, feature, structure or characteristic describedin connection with the embodiment is included in at least one embodimentof the teaching. References to a particular embodiment within thespecification do not necessarily all refer to the same embodiment.

The following discussion will make reference to exemplary embodiments asshown in the accompanying drawings. While various embodiments andexamples are described, it is not intended that the invention be limitedto such embodiments. On the contrary, the invention contemplates variousalternatives, modifications and equivalents, as will be appreciated bythose of skill in the art. Those of ordinary skill will recognizeadditional implementations, modifications and embodiments, as well asother fields of use, which are within the scope of the presentdisclosure as described herein.

A column for LC analysis is usually in the form of a packed bed or is anopen tubular column. The column contains a stationary phase, that is, amaterial for which the components to be separated have varyingaffinities. A mobile phase of the chromatographic process is generally asolvent or mixture of solvents into which the sample to be analyzed isinjected. The mobile phase enters the column and the sample adsorbs ontothe stationary phase. The solvent or solvent mixture is not adsorbed onthe stationary phase and instead passes through the column. It should benoted that the word “column” as used herein generally means any deviceor component that contains the stationary phase and is not intended tolimit embodiments to columns of any particular construction, numberconfiguration, width or diameter. For example, in some embodiments thecolumn can be formed according to a variety of geometries on amicrofluidic substrate.

In some binary solvent delivery systems a first pump draws a firstsolvent from a tank and supplies the first solvent at a desired flowvelocity and pressure to a T-shaped piping connector. A second pumpdraws a second solvent from a second tank and supplies the secondsolvent at a desired flow velocity and pressure to the T-shaped pipingconnector. The solvents are blended at the connector to achieve asolvent mixture having desired properties. The flow rate of each solventcan be adjusted to vary the composition of the solvent mixture overtime. A variation in the solvent mixture over time is referred to as asolvent or compositional gradient.

As the mobile phase passes through the column, different components inthe mobile phase adsorb to the stationary phase to varying degrees.Components with a strong attraction to the stationary phase move moreslowly through the column than components with a weak attraction. Thusthe components are separated according to the different speeds ofmovement through the column and elute from the column at differenttimes. The component with the least affinity for the stationary phaseelutes first, while the component with the greatest affinity for thestationary phase elutes last. A detector analyzes the emerging stream bymeasuring a property that is related to the concentration andcharacteristic of chemical composition. By way of specific examples, themeasured property can be the refractive index or ultra-violetabsorption.

Some chromatographic systems utilize a column heater to control columntemperature. For example, the column may be located in a temperaturecontrolled chamber such as a convection oven or a chamber employingresistance heating. The control of column temperature is important tothe resolving efficiency of a liquid-chromatography column, whether thesystem is designed to operate isothermally or by temperature programmedanalysis. In particular, the retention time and peak shape vary inresponse to changes in the column temperature.

If the temperature of the mobile phase supplied to the column is notconstant, for example, for long (e.g., multi-hour) chromatographic runswhere the variations in room temperature are significant, the accuracyof the chromatographic analysis can degrade. A device to pre-heat themobile phase is sometimes used to reduce temperature fluctuations at thecolumn inlet.

Traditional high-performance liquid chromatography (HPLC) techniqueshave typically utilized analytical columns constructed fromstainless-steel tubing having an inner bore diameter of 4.6 mm andlengths in a range of about 5 cm to about 25 cm. To complete ananalytical column for a HPLC instrument, a fritted end-fitting istypically attached to a piece of tubing, and the tubing is then packedwith particles such as silica-based particles that are functionalizedwith a variety of functional moieties.

The flow rate of the mobile phase is important for achieving optimalseparation efficiency using the completed column. For a 4.6 mm diametercolumn packed with 5 μm diameter particles, a desirable flow rate istypically between about 1 mL/min and about 2 mL/min. To maintainseparation efficiency, it is also desirable to minimize the presence ofunswept dead volume in the plumbing of the HPLC instrument.

In a HPLC instrument, an injector is typically used to inject a sampleinto a flowing mobile phase as a discrete fluidic plug. Dispersion of aplug band traveling to and/or from the column reduces the efficiency ofthe chromatographic system. For example, in a chromatographic systemusing 4.6 mm column tubing and a mobile phase flowing at 1 mL/min to 2mL/min, tubing having an outer diameter of 1/16 inch and an innerdiameter of about 0.010 inch is typically used to plumb connectionsbetween the various HPLC components (e.g., pump, injector, column anddetector). For these flow rates and tubing dimensions, it is relativelyeasy to machine port details to tolerances that ensure minimal bandbroadening at tubing interfaces.

A desire to reduce the consumption of the mobile phase solvent hasmotivated a trend to reduce the inner diameter of the column. Thusdifferent scales of chromatography are now commonly practiced. These aretypically defined according to Table 1 where “ID” indicates innerdiameter.

TABLE 1 HPLC Scale Column ID Typical Flow range Analytical 4.6 mm   1'smL/min Microbore/UPLC 1-2 mm 100's μL/min

Microbore HPLC is often practiced with equipment similar to that usedfor analytical scale HPLC with minor modifications. Although additionalcare is generally taken when making fittings, microbore HPLC typicallyrequires an operating skill level similar to that of analytical scaleHPLC.

Ultra performance liquid chromatography (UPLC) is generally performedwith traditional microbore columns (2.1 mm ID); however, packingmaterial with particle diameters less than 2 μm are commonly used. Thesmaller particle sizes result in higher column efficiency and enableoperation with a higher separation speed. Advantageously, the smallercolumn dimensions permit lower volumetric flow rates while reducing runtime and yielding a more efficient separation with improved resolution.

While a primary motivation to replace analytical-scale HPLC withmicrobore-scale HPLC and UPLC is often a desire to reduce solventconsumption, the main benefits of such transfers are improvements inspeed of analysis, chromatographic resolution and sensitivity.Consequently, transferring a method from a HPLC system to a UPLC systemshould ensure that the selectivity of the separation is preserved whilespeed, resolution and sensitivity are enhanced. The selectivity of theseparation is described by the relative retention times of the peakswithin the chromatogram or by the separation factor α between adjacentpeaks. The selectivity is primarily determined by the composition of themobile phase, the specific stationary phase bonded to the column and theinternal temperature of the column. Adjustment of flow rates andgradient composition to preserve the selectivity is principallydetermined by the geometry of the columns, the relative particlediameters of the columns and the system volumes of the chromatographs.

The role of column temperature in the control of retention times and theselectivity of separations is recognized as an important factor inperforming reproducible separations. A principal aspect to performingreproducible separations is the ability to transfer a chromatographicmethod between different chromatographic systems. It may be desirable totransfer a method from a HPLC system to a UPLC system or from a UPLCsystem to a HPLC system. Alternatively, it may be desirable to transferto another chromatographic system having a different column and/ordifferent column chemistry.

Different chromatographic systems typically incorporate column ovens ofdifferent design, in part, to ensure that retention times and separationmetrics (e.g., selectivity, peak shape and column efficiency) remainstable while the ambient temperature varies. A common assumption is thatthe oven temperature and the average internal column temperature are thesame. The characterization of a column heater (or cooler) can beperformed by measuring the temperature of the column heater at aspecified location with a calibrated thermometer or temperature probe;however, this technique does not accurately indicate the internaltemperature of the column under chromatographic conditions. Inparticular, column heaters or coolers operating according to differentdesign principles frequently exhibit different retention behavior whenset to the same nominal temperature even if both column heaters providethe same temperature accuracy when measured by an external thermometer.

In UPLC systems, the use of particles smaller than 2 μm leads tosignificant frictional heating as a result of the pressure-volume workdone on the column. Additionally, it is important that the UPLC columnbe operated in an oven which does not circulate the heating fluid (e.g.,air) in order to preserve the separation efficiency. When UPLC columnsare operated in column ovens with convective circulation of air, radialthermal gradients are induced within the column. The radial thermalgradients degrade the efficiency of the separation and can lead to splitpeaks for single components. Because convection ovens degrade theseparation efficiency of UPLC columns, the effectiveness of devices usedto pre-heat the mobile phase become significant in UPLC. In HPLC, theabsence of significant frictional heating (smaller column backpressure)permits the use of convection ovens for column heating and theperformance of inlet preheating is less critical to column temperaturecontrol.

Consequently, the assumption that the oven set temperature and theaverage internal column temperature are the same is generally invalid,especially when the column ovens may differ in their operatingprinciples and efficacy of the inlet preheater. The resultingdifferences in the internal column temperatures can result indifferences in retention and resolution that can compromise theequivalency of test results.

In various embodiments, the method of the invention enables separationsto be performed using different chromatography systems with reproducibleand equivalent results. For example, the method allows for achromatography method developed for HPLC to be more readily transferredto a UPLC system and for a chromatography method developed for a UPLCsystem to be more readily transferred to a HPLC system. The methodaccommodates column ovens of different design in which the internalcolumn temperatures are not equal although the operating temperatures ofthe column ovens may be accurately controlled to equal values. Themethod causes the retention behavior and resolution of differentchromatography systems to be substantially the same, resulting in anequivalency of separation results.

Although the embodiments described below relate primarily to control ofcolumn temperature by column ovens or heaters, it should be recognizedthat other embodiments according to the principles of the invention arebased on control of the temperature of a column by a cooler or by atemperature control system capable of both heating and cooling a column.

The effect of column temperature on chromatographic measurements isoften based on an analysis of van't Hoff plots as is known in the art.One assumption in the generation of van't Hoff plots is that thetemperature which controls the partitioning of a solute between thestationary and mobile phases is the set temperature of the column oven.In chromatographic systems, the temperature varies with location withinthe column. At the column inlet, the primary effect on the temperatureis the temperature of the incoming mobile phase which is heated eitherpassively with a heat exchanger connected to the column oven or activelywith a separately controlled heat exchanger. At the column outlet, theprincipal source of heat is based on frictional heating occurring withinthe column. As particle size decreases from a typical 5 μm particle inconventional HPLC to sub 2 μm in UPLC, the significance of frictionalheating associated with higher backpressures increases.

When column backpressures are low the contribution of frictional heatingis less significant. Under such conditions, the mechanism of heattransfer within the column oven leads to significant differences in theeffective temperature of the column. Various column ovens employ forcedconvection of heated or cooled air, circulating water jackets and, insome applications, are based on passive heat transfer in an oven with noactive air circulation. Each design configuration typically yieldslinear van't Hoff plots and precise control of retention time. Moreover,each design configuration can provide an accurate temperature at aselected location within the column oven where the temperature ismeasured with a calibrated thermometer such as a thermocouple orthermistor. However, retention factors typically differ among columnovens especially when the design principles are not the same althoughidentical columns and premixed mobile phases may be used.

Equation (1) is one form of the van't Hoff equation where K is theequilibrium constant for partitioning, k′ is the retention factor and θis the phase ratio.ln(K)=ln(k′)−ln(θ).   (1)The right side of the equation can be rewritten as follows:ln(k′)−ln(θ)=−1/RT*ΔG°  (2)where R is the gas constant, T is the absolute temperature in Kelvin andΔG° is the Gibbs free energy. Equations (1) and (2) can be used toderive the following relationship:ln(k′)=−[ΔG°/R]*(1/T)+ln(θ).   (3)

The van't Hoff functional relationship provided in equation (3) can begraphically represented for a particular solute as a plot of ln(k′) as afunction of inverse temperature T. In general such van't Hoff plots arelinear. Variations from linearity are typically associated with poorheat transfer at higher temperatures and higher flow rates, or withfrictional heating at lower temperatures where a high solvent viscosityresults in a significant pressure drop across the analytical column.

If the van't Hoff plots for the components of a mixture are parallel ordo not intersect in the temperature range of an LC system, adjustment ofthe set temperature of the column oven is straightforward because theorder of elution of the components does not change and relativeretention metrics are typically well preserved. In that case, thetemperature is incremented to ensure that the retention factor k′ isheld constant for each of the critical components of the sample.

In contrast, when the van't Hoff plots intersect, the componentsco-elute at the temperature corresponding to the intersection point,that is, the components co-elute at an “isoretention temperature.” Inaddition, the order of elution reverses as the column temperaturetransitions through the isoretention temperature. This can result inmisidentified peaks as well as incomplete separations of critical peakpairs.

By way of example, FIG. 1 shows how the retention times for two solutesA and B decrease with increasing temperature. In this example, theisoretention temperature is slightly less than 60° C. Solute A elutesbefore a solute B for temperatures less than the isoretentiontemperature while solute A elutes after the second solute B fortemperatures greater than the isoretention temperature. The two solutesA and B co-elute when the column temperature is maintained at theisoretention temperature. The possibility of a reversal of the order ofelution, or “peak order reversal”, with a change in column temperaturecan be problematic for unknown peaks within a chromatogram especiallywhen the set temperature of the column is nearly equal to theisoretention temperature for the corresponding solutes.

At the intersection point of two van't Hoff plots, the separation factorα, defined as the ratio (k_(B)′/k_(A)′) of the respective retentionfactors, is one and the phase ratio θ is eliminated. Thus equation (3)can be expressed asT _(iso) =[ΔH° _(B) −ΔH° _(A) ]/[ΔS° _(B) −ΔS° _(A)]+φ(t)   (4)where ΔH°_(A) and ΔH°_(B) are the enthalpy changes associated with thepartitioning of compounds A and B, respectively, and ΔS°_(A) and ΔS°_(B)are the entropy changes associated with the partitioning of compounds Aand B, respectively. φ(t) is an error term that incorporates all of thenon-equilibrium contributions to the isoretention temperature T_(iso).Ideally, φ(t) has a small value (e.g., less than 1° C.) and does nothave a strong dependence on temperature. The isoretention temperatureT_(iso) is a property of the interaction of the solutes with thestationary and mobile phases and equation (4) includes the error termassociated with the measurement. The isoretention temperature can bedetermined by plotting the two van't Hoff plots and determining theintersection point. Alternatively, the isoretention temperature can beestablished by determining the temperature of co-elution, that is, thetemperature at which the separation factor α has a value of one. In manyinstances, the second approach is a more efficient and convenientapproach.

If frictional heating does not contribute significantly to the internalcolumn temperatures, separations performed for two differentchromatography systems each using the same type of column, same solutepair and same mobile phase conditions can be used to relate theeffective column temperatures. In particular, the difference in theisoretention temperatures is a measure of the difference in the averageinternal column temperatures, or effective column temperatures, for twoLC systems set to the same column temperature.

FIG. 2 shows a flowchart representation of an embodiment of a method 100for determining a difference in isoretention column temperatures for twochromatographic systems according to the invention. The difference inthe average column temperature can be used to transfer a chromatographymethod between two LC systems that differ in design principle andimplementation.

A first LC system is used to determine (step 110) an isoretentiontemperature T_(ISO) _(—) ₁ for two solutes. A second LC system employingthe same type of column and mobile phase conditions is used to determine(step 120) an isoretention temperature T_(ISO) _(—) ₂ for the same twosolutes. The difference in the isoretention temperatures ΔT_(ISO) of thetwo LC systems is determined (step 130) and can subsequently be used totransfer a chromatography method from one of the LC systems to the otherLC system. In particular, if the isoretention temperature T_(ISO) _(—) ₁of the first LC system is greater, to transfer a chromatographic methodfrom the first system to the second LC system, the column temperaturefor the second LC system is set to a value that is less than the columntemperature previously used for the chromatography method of the firstLC system by the difference ΔT_(ISO). Conversely, if the isoretentiontemperature T_(ISO) _(—) ₁ of the first LC system is less, to transfer achromatographic method from the first LC system to the second LC system,the column temperature for the second LC system is set to a value thatis greater than the column temperature for the chromatography method ofthe first LC system by the difference ΔT_(ISO).

To accurately transfer chromatography methods between LC systems, it ispreferable to ensure that the column temperature set for a separation isnot significantly different from the determined isoretentiontemperatures. Thus the ability to transfer chromatographic methods maybe limited to a small column temperature range (e.g., within ±10° C.).

For example, to transfer a separation carried out on a first LC systemwith a set temperature of 65° C. to a second LC system, it is desirableto choose a solute pair which has an isoretention temperature that isclose to 65° C. This ensures that the differences in the performance ofthe inlet preheaters of both systems are accurately modeled. By way ofexample, FIG. 3 (described in more detail below) suggests that theisoretention temperature of 63° C. for the solutes TNT and 4-amino DNT(63° C.) is a suitable choice.

To expand the range of temperatures for transferring chromatographymethods, steps 110 to 130 of the method 100 can be repeated usingdifferent pairs of solutes. Thus isoretention temperatures T_(ISO) _(—)₁ and T_(ISO) _(—) ₂ can be determined for each LC system for a numberof pairs of solutes and the difference in the isoretention temperaturesfor a common pair of solutes can be used to transfer a chromatographymethod from one LC system to the other for a limited range oftemperatures (e.g., ±10° C.) about the determined isoretentiontemperature. Preferably, the selections of the solute pairs used todetermine isoretention temperatures are made to obtain isoretentiontemperatures that span a large temperature range to thereby reducelimitations on temperatures than can be utilized in the transfer ofchromatography methods between LC systems. In some embodiments, eachsolute pair is a separate injection into the LC system. In alternativeembodiments, at least two solute pairs are present in at least one ofthe injections thereby reducing the time and effort necessary to obtainthe distribution of isoretention temperatures for the LC system.

Some solutes may be paired with more than one other solute. For example,solute A and solute B may be used to determine one isoretentiontemperature while solute A and solute C can be used to determine adifferent isoretention temperature. FIG. 3 graphically illustrates theseparation factor α as a function of column temperature for four solutepairs selected from a set of four nitrotoluene standards:2,4,6-trinitrotoluene, 2,4-dinitrotoluene, 2-amino,4,6-dinitrotolueneand 4-amino,2,6-dinitrotoluene (“TNT”, “DNT”, “2Amino” and “4Amino”,respectively). The isoretention temperature for each solute pair isdetermined as the temperature at which the separation factor α for thesolute pair has a value of one. The relatively small change in the slopeof the plots between adjacent data samples allows linear interpolationto be applied to determine the isoretention temperatures withoutintroducing substantial error. From the plots, the isoretentiontemperatures for 2Amino and DNT, 4Amino and DNT, 2Amino and TNT, and4Amino and TNT for the subject LC system are determined to be 31.4° C.,41.7° C., 57.5° C. and 63.9° C., respectively. Thus the fournitrotoluene standards cover a significant portion of the columntemperature range of many HPLC and UPLC systems.

To transfer from the LC system associated with the data in FIG. 3 toanother LC system (or from another LC system to the subject LC system),the isoretention temperatures of the other LC system are similarlydetermined, and the matched isoretention temperatures (i.e.,isoretention temperatures for the same solute pair) of the two LCsystems that are closest in value to the desired column temperature forthe separation to be performed are differenced to determine theappropriate column offset temperature for performing the separation.

Other solutes can be used to generate a number of isoretentiontemperatures for LC systems. In some instances, the particular solutesemployed may exhibit more complex behaviors. Consequently, variousalternative techniques for peak identity tracking may be preferred sothat the user can determine the retention time of each solute at eachtemperature. For example, manipulation of the relative amounts of eachsolute may be desired as well as the use of multiwavelength detection orspectroscopic measurements to achieve a finer peak tracking resolution.

FIG. 4 shows a flowchart representation of another embodiment of amethod 200 for determining a difference in average column temperaturesfor two chromatographic systems according to the invention. Accordingly,a first LC system is used to determine (step 210) a van't Hofffunctional relationship for a solute. More particularly, the natural logof the retention factor k′ is determined as a function of inverse columntemperature T. Similarly, the first LC system is used to determine (step220) the van't Hoff functional relationship of a second solute using thesame column and mobile phase.

Using the two van't Hoff functional relationships, an isoretentiontemperature T_(ISO) _(—) ₁ for the two solutes is determined (step 230).The two van't Hoff functional relationships may be plotted orgraphically displayed and the isoretention temperature T_(ISO) _(—) ₁determined by identifying the column temperature at the intersection ofthe two plots.

A second LC system is used to determine (steps 240 and step 250) thevan't Hoff functional relationships for the same two solutes used withthe first LC system. An isoretention temperature T_(ISO) _(—) ₂ isdetermined (step 260) from the two van't Hoff functional relationshipsfor the second LC system. The difference ΔT_(ISO) of the isoretentiontemperatures T_(ISO) _(—) ₁, and T_(ISO) _(—) ₂ of the first and secondLC systems is determined (step 270) and can be used as the column offsettemperature to adjust for the transfer of a chromatographic methodbetween the two LC systems as described above. In particular, thedifference ΔT_(ISO) is an offset that is applied (step 280) to the setpoint of the column temperature of the LC system that is to perform thetransferred chromatographic method.

The method 200 can be applied to other pairs of solvents to determineother isoretention temperatures. For example, FIG. 5 graphically depictsthe van't Hoff functional relationships for the four solutes of FIG. 3.The four isoretention temperatures 31.4° C., 41.7° C., 57.5° C. and63.9° C. are determined from the four points A, B, C and D,respectively, at which the linear plots for two solutes intersect. Itshould be noted that that the graphical data in FIGS. 3 and 5 aremathematically related, that is, the data shown in FIG. 3 can be derivedfrom the data of FIG. 5 and, conversely, the data shown in FIG. 5 can bederived from the data of FIG. 3. The van't Hoff plots of FIG. 5 enablelinear interpolation to be used to accurately determine the fourisoretention temperatures for the four solute pairs.

Preferably, when transferring a chromatographic method from between twoLC systems, the isoretention temperatures for both LC systems for acommon solute pair that are closest to the desired column temperaturefor the separation to be performed are used to determine the differenceΔT_(ISO). The difference ΔT_(ISO) is applied as an offset for the columnset temperature of the LC system relative to the column set temperatureused with the other LC system.

While the invention has been shown and described with reference tospecific embodiments, it should be understood by those skilled in theart that various changes in form and detail may be made therein withoutdeparting from the spirit and scope of the invention as recited in theaccompanying claims.

What is claimed is:
 1. A method of transferring a chromatographic method between liquid chromatography (LC) systems, the method comprising: determining an isoretention temperature of a first LC system at which a first solute and a second solute in a mobile phase of the first LC system co-elute from a column; determining an isoretention temperature of a second LC system at which the first solute and the second solute in a mobile phase of the second LC system co-elute from a column; and determining a column offset temperature for transferring a chromatographic method between the first and second LC systems based on the difference in the isoretention temperatures of the first and second LC systems.
 2. The method of claim 1 further comprising controlling a column temperature for a column in the first LC system in response to the column offset temperature.
 3. The method of claim 2 further comprising: performing a separation on a sample using the first LC system at a first column temperature; and comparing results of the separation with results of a separation performed on the second LC system at a second column temperature, wherein a difference of the first and second column temperatures is equal to the column offset temperature.
 4. The method of claim 1 wherein one of the first and second LC systems is a high-performance liquid chromatography (HPLC) system and the other of the first and second LC systems is a UPLC system.
 5. The method of claim 1 wherein the column of the first LC system and the column of the second LC system are identical columns.
 6. The method of claim 1 wherein the mobile phases of the first and second LC systems are identical mobile phases.
 7. The method of claim 1 wherein a column of each of the first and second LC systems has a thermal gradient and wherein the first and second isoretention temperatures are average internal column temperatures.
 8. The method of claim 1 wherein the steps of determining an isoretention temperature of a first LC system, determining an isoretention temperature of a second LC system and determining a column offset temperature are repeated one or more times to thereby determine a plurality of column offset temperatures.
 9. The method of claim 8 further comprising: performing a separation on the first LC system at a first column temperature; and comparing results of the separation with results of a separation performed on the second LC system at a second column temperature, wherein a difference of the first and second column temperatures is equal to the column offset temperature.
 10. A method of transferring a chromatographic method between liquid chromatography (LC) systems, the method comprising: determining, for a plurality of solute pairs each having a first solute and a second solute, an isoretention temperature of a first LC system at which the first solute and the second solute in a mobile phase of the first LC system co-elute from a column; determining, for each of the solute pairs, an isoretention temperature of a second LC system at which the first solute and the second solute in a mobile phase of the second LC system co-elute from a column; and determining, for each of the solute pairs, a column offset temperature for transferring a chromatographic method between the first and second LC systems based on the difference in a respective pair of isoretention temperatures of the first and second LC systems.
 11. The method of claim 10 further comprising controlling a column temperature for a column in the first LC system in response to one of the column offset temperatures.
 12. The method of claim 10 further comprising: performing a separation on a sample using the first LC system at a first column temperature; and comparing results of the separation with results of a separation performed on the second LC system at a second column temperature, wherein a difference of the first and second column temperatures is equal to one of the column offset temperatures.
 13. The method of claim 12 wherein the difference of the first and second column temperatures is equal to the column offset temperature based on the isoretention temperatures of the first and second LC systems that are closest in value to at least one of the first column temperature and the second column temperature.
 14. A method of transferring a chromatographic method between liquid chromatography (LC) systems, the method comprising: determining a van't Hoff functional relationship for a first solute in a mobile phase for a plurality of column temperatures for a first LC system; determining a van't Hoff functional relationship for a second solute in a mobile phase for a plurality of column temperatures for the first LC system; determining an isoretention temperature of the first LC system for the first and second solutes as a temperature at which a retention factor of each of the van't Hoff functional relationships of the two solutes in the first LC system are equal; determining a van't Hoff functional relationship for the first solute in a mobile phase for a plurality of column temperatures for a second LC system; determining a van't Hoff functional relationship for the second solute in a mobile phase for a plurality of column temperatures for the second LC system; determining an isoretention temperature of the second LC system for the first and second solutes as a temperature at which a retention factor of each of the van't Hoff functional relationships of the two solutes in the second LC system are equal; and determining a column offset temperature for transferring a chromatographic method between the first and second LC systems based on the difference in the isoretention temperatures of the first and second LC systems.
 15. The method of claim 14 further comprising controlling a column temperature for a column in the first LC system in response to the column offset temperature.
 16. The method of claim 15 further comprising: performing a separation on a sample using the first LC system at a first column temperature; and comparing results of the separation with results of a separation performed on the second LC system at a second column temperature, wherein a difference of the first and second column temperatures is equal to the column offset temperature.
 17. A method of transferring a chromatographic method between liquid chromatography (LC) systems, the method comprising: determining, for a plurality of first solutes, a van't Hoff functional relationship for the first solute in a mobile phase for a plurality of column temperatures for a first LC system; determining, for a plurality of second solutes, a van't Hoff functional relationship for the second solute in a mobile phase for a plurality of column temperatures for the first LC system; determining, for a plurality of solute pairs each comprising one of the first solutes and one of the second solutes, an isoretention temperature of the first LC system as a temperature at which a retention factor of the van't Hoff functional relationships of the first and second solutes in the first LC system are equal; determining, for the plurality of first solutes, a van't Hoff functional relationship for the first solute in a mobile phase for a plurality of column temperatures for a second LC system; determining, for the plurality of second solutes, a van't Hoff functional relationship for the second solute in a mobile phase for a plurality of column temperatures for the second LC system; determining, for the plurality of solute pairs, an isoretention temperature of the second LC system as a temperature at which the retention factor of the van't Hoff functional relationships of the first and second solutes in the second LC system are equal; and determining, for each of the solute pairs, a column offset temperature for transferring a chromatographic method between the first and second LC systems based on a difference in a respective pair of isoretention temperatures of the first and second LC systems.
 18. The method of claim 17 further comprising controlling a column temperature for a column in the first LC system in response to one of the column offset temperatures.
 19. The method of claim 17 further comprising: performing a separation on a sample using the first LC system at a first column temperature; and comparing results of the separation with results of a separation performed on the second LC system at a second column temperature, wherein a difference of the first and second column temperatures is equal to one of the column offset temperatures. 